A Mad World, my Master, Dr. Percy

With apologies to Thomas Middleton, I want to ask the philosophy-minded contributors to this forum to consider the question: What is distance?

The concept of distance seems fundamental in Physics, because without it coordinate systems can’t be set up and similar abstractions like the Spacetime of Relativity {either Special (SR) or General (GR)}, can’t be defined. We all have a pretty good practical idea what distance is, but there are variations. Here I list the possible perspectives of several observers:

Joe Folks wants to drive from New York City to Chicago. From a road atlas he finds that the
distance is 792 miles, as once determined using theodolites, triangulation methods and Euclidean geometry, allowing for Earth’s spherical shape. Joe also estimates his driving time to be 13 hours, and may prefer to say that Chicago is just 13 hours out of NYC .

Fiona Physics knows that the distance to Innes’ star Proxima Centauri is 4.22 light years, because astronomers have measured its parallax and calculated its distance, assuming Euclidean geometry and a constant speed of light, c. But she also knows from SR that she could get to this star in any chosen travel time (measured by her watch) less than 4.22 years, say in 13 hours, on a Centauri- bound spaceship measured by us to be passing the Earth at a speed appropriately near to c. She could then claim that Proxima Centauri is 13 hours “out of Earth”.

Kim Cosmo quibbles about the underpinnings of these distance estimates. She imagines, for the purposes of discussion, a Lambda CDM universe in which NYC and Chicago, or the Earth and Proxima Centauri, are just labeled point locations in Local Inertial Frames, perhaps at rest relative to local ‘ethers’ defined by local Cosmic Microwave Backgrounds. In this case just how are ‘distances’ to be measured as the universe ‘expands’? Not by maps in an old atlas, or globally by methods that use Euclidean geometry. Kim could say that distance is proportional to the (constant) number of wavelengths in a ray of monochromatic light linking the points. Or that distance is c times an (increasing) photon travel time, making sure to specify the timing clock. She could even argue that distance is given by‘rigid’ measuring rods.

Joe, Fiona and Kim all use the word “is” with seemingly equal justification. What does "is" mean in this multiple context? And does this validate the operational method of defining things, as in the physics “philosophy” of Dr Percy Bridgman?

Many people ask what time is, few people ask what space (or distance) is. Of course the latter question merits as much attention as the former. Like most people, it has not occupied my own mind so much. At first glance, common understanding gives me this rather banal view:

Distance or length: a difference between two positions or points.
Position or point: a coordinate in space.
Space: a field or expanse perceived by our senses (and measuring instruments).

So distance is a difference between two coordinates in an expanse we are able to perceive. This may or may not be anywhere near what you are looking for...

Distance is completely relative, and you need a bunch of references to understand it.
You can reference seconds, minutes, hours, meters and even amount of atoms in the distance you are measuring.

But beyond that distance is also a subjective phenomena, one that we have because our minds create a space where distance exists as an abstraction.
Like everything else in reality, I think we must first realize that reality is what it is, and everything we know about reality stems from systems we create in our heads.
These systems include all the stimuli, and all the processing of the stimuli via the brain.

With distance, without referencing minutes, seconds, meters (etc) or our subjectively created space, we can say nothing about distance.
The same can be said about just about any physical phenomena or object I think.

What this tells ME anyway, is that our subjective experience can never directly be explained with words, math or any system, we will always be abstracting it with references, and that distance, like everything else, is a higher level of abstraction.

I hope that makes sense to people. (I almost lost myself too, feel free to correct anything you disagree with )

...distance is a difference between two coordinates in an expanse we are able to perceive......

Thanks for this. But what then are coordinates? Numbers assigned to a point? Like the mathematician's definition of a point in the R3 space of vector algebra --- a set of three real numbers? Sadly, real numbers are just Greek inventions, extending earlier folks' inventions of first, counting numbers and later, rational numbers. One is then carried back to the difficult questions about the nature of numbers (and perhaps 'expanse').

Operational definitions are, I believe, easier to understand. See for example Bridgman's approach , which I recommend. For instance, my own definition of 'expanse' would be 'that in which you can swing a cat'!

I'm more concerned with using the word "is" in defining 'distance', which seems to me have several operational definitions.

Distance is completely relative
....distance is also a subjective phenomena.... we can say nothing about distance......we will always be abstracting it with references, and .... distance, like everything else, is a higher level of abstraction.

I hope that makes sense to people. (I almost lost myself too, feel free to correct anything you disagree with )

You almost lost me too, but thanks. I don't quite agree that 'we can say nothing about distance'. What about this stuff of Bridgman's about length, which is closely related:

Percy Bridgman on the concept of length said:

Our task is to find the operations by which we measure the length of any concrete physical object.....such as a house ..... We start with a measuring rod, lay it on the object so that one of its ends coincides with one end of the object, mark on the object the position of the other end of the rod, then move the rod along in a straight line extension of its previous position until the first end coincides with the previous position of the second end, repeat this process as often as we can, and call the length the total number of times the rod was applied......

Mental representations that allow you to identify these different positions in any manner your mind sees fit. They could be numbers. They could be labels such as "here" and "there". Anything that lets your mind record the reality that there is a difference.

I'm more concerned with using the word "is" in defining 'distance', which seems to me have several operational definitions.

Without any linguistic background to qualify my answer (not something that has ever stopped me), the word seems to indicate a correspondence between an aspect of reality and our mental representation of it.

Thanks again for the help. Try this : link If it doesn't work, blame it on me; its a Marxist site, and maybe I'm jinxed by it. Googling Percy Bridgman will help, though. Percy (R.I.P.) is a bit of a philosopher who did win a Physics Nobel. He seems also to have bypassed most the gobbledygook in philosophy that intimidates me.

Your three observers all perceive a difference between "here" and "there" in various contexts. Their use of "is" is personal to them of course. But in all cases, "is" represents a correspondence between reality and their perception of it. This is the same as one person saying "it is cold here" and another person saying "it is hot here". They are both right in their testimony.

Your three observers all perceive a difference between "here" and "there" in various contexts. Their use of "is" is personal to them of course. But in all cases, "is" represents a correspondence between reality and their perception of it. This is the same as one person saying "it is cold here" and another person saying "it is hot here". They are both right in their testimony.

Thanks for putting so clearly what I now assume is the view of at least one philosopher. You've almost destroyed my faith in Physics with this subjective and internal view! I think that most physicists assume that there is a real, objective, tangible world out there. In fact the world, or universe, if it exists, presents many faces to 'objective' observers, try as they will to retain their belief in its concrete character. The three characters I invented exemplify this ambiguity,which emerges even when one considers as basic a concept as 'distance'.

If one adopts an operational perspective, which I recommend, one ducks the whole nebulous issue and accepts that the best one can do is to describe the 'outer realities' in terms that others can understand.

Amazing that such descriptions are so often to our material advantage, isn't it?

You've almost destroyed my faith in Physics with this subjective and internal view!

Ha! Well, it may not be a bad thing since faith and science don't really go hand in hand. But it's not wrong to take a position from one's own point of view, as Albert was saying. And in the end, the only science that matters to you is the one that works from your own point of view.

You almost lost me too, but thanks. I don't quite agree that 'we can say nothing about distance'. What about this stuff of Bridgman's about length, which is closely related:

Yeah but then you are applying some external object.
I did say

With distance, without referencing minutes, seconds, meters (etc) or our subjectively created space, we can say nothing about distance.

And the rod is analog to meters etc.

The problem is, the rod in your example has no corrolation to the house.
We need to actively remember how many times we applied the rod to measure the length.
An example would be the whole is math created or discovered discussion.
Reality, without observers, is at any given moment in time, a constant and completely 'true' system. Everything that exists in the universe exists together, in some sort of system.
I propose that we will never truly see these systems, but we will rather have to apply our own systems dynamically depending on the state of the universe.

When I say that we can say nothing about distance, I just mean we can't say anything about it without some sort of system, whether it is math, english language, or our abstract subjective thoughts.

In this hypothesis, one could also say that these systems humans create, every facet that we experience as reality is an abstracted version of reality, it's not really /the/ reality.
On the other one can say that all this IS reality, because humans and subjective thoughts ARE reality, but then we're going into soupy branches of thought that are not suiting for this thread.

When I say that we can say nothing about distance, I just mean we can't say anything about it without some sort of system, whether it is math, english language, or our abstract subjective thoughts.

I agree -- I misunderstood your meaning, which I take is that one can't describe distance to someone else without using a language, either English or mathematics, or think about it yourself without using your own mental constructs. Very true. I apologise.

In this hypothesis, one could also say that these systems humans create, every facet that we experience as reality is an abstracted version of reality, it's not really /the/ reality.
On the other one can say that all this IS reality, because humans and subjective thoughts ARE reality, but then we're going into soupy branches of thought that are not suiting for this thread.

I agree here too. I also don't want to land this thread 'in the soup', as it were.

It seems to me that most of the trouble lies in using the word "is", as if its use excludes alternative descriptions. It is often correct to say something like "that dog is black", meaning that you're excluding descriptions like white or red, etc. But in saying "distance is...., and competing the sentence with a single description, one is oversimplifying. The concept of "distance" is 'different strokes for different folks', a fact that even physics folk often don't always appreciate.